If I wanted to set up a company to receive payments from Kindle (and other platforms I guess) would I just change my payment details, or would it be possible to create a second KDP account for this purpose?

I'm trying to determine whether I could publish some books under a company account, and some under an individual account.

What Amazon wants is a tax # and a bank account. If you're planning to have a company EIN and a bank account separate from those of your regular name, then I guess make two Amazon accounts.

I do have a company name and EIN, but I only publish under that. I do use two company names, but they both feed into the same bank account, and I report my taxes under the same EIN (one company name is a DBA, "doing business as," name of the other).

You can be John Smith, though, with your regular SSN and bank account, and publish some books under John Smith and some under Pocanhontas Press, Inc., and still have the money go to John Smith.

However, state laws for things like LLCs and DBAs and all that vary. I suggest talking to someone who prepares taxes in your state and just making sure that you're doing everything correctly. Someone here could tell you what was legal in their state, and it could still be different in your state (like in some states, you need to file an official DBA, I think).

I have owned small businesses all my life, and all I have ever needed, both for the IRS and my state, is a SS#. The state does require a fictitious name registration if yo use a business name other than your own last name. That is $50 for five years, and it is just so you can deposit checks into your bank account that have been written out to your company name and not your own name. (The bank account will be a DBA.) If you have no employees, your SS# is all you need for a sole proprietorship. If all you are doing is starting a publishing company in an attempt to hide the fact you are self-published, I see no reason why you would need employees.